Abstract: In this paper we study two families of functions, viz. F and H, and show how to approximate the functions considered in the interval [0,1 ]. The functions are assumed to be real when the argument is real.

We define

The approximations are defined in the interval [0,1 ] by

and

where .

The associated matrices are analyzed using the theory of orthogonal polynomials, especially the Jacobi polynomials . We apply the general theory to the basic trigonometric functions and .